TY - JOUR
T1 - Existence of Solutions to a super-Liouville equation with Boundary Conditions
AU - Han, Mingyang
AU - Wu, Ruijun
AU - Zhou, Chunqin
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.
PY - 2025/6
Y1 - 2025/6
N2 - In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemann surface M with boundary and with its Euler characteristic χ(M)<0. The boundary condition couples a Neumann condition for functions and a chiral boundary condition for spinors. Due to the generality of the equation, we introduce a weighted Dirac operator based on the solution to a related Liouville equation. Then we construct a Nehari manifold according to the spectral decomposition of the weighted Dirac operator, and use minimax theory on this Nehari manifold to show the existence of the non-trivial solutions.
AB - In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemann surface M with boundary and with its Euler characteristic χ(M)<0. The boundary condition couples a Neumann condition for functions and a chiral boundary condition for spinors. Due to the generality of the equation, we introduce a weighted Dirac operator based on the solution to a related Liouville equation. Then we construct a Nehari manifold according to the spectral decomposition of the weighted Dirac operator, and use minimax theory on this Nehari manifold to show the existence of the non-trivial solutions.
UR - http://www.scopus.com/inward/record.url?scp=105006729839&partnerID=8YFLogxK
U2 - 10.1007/s00526-025-03024-3
DO - 10.1007/s00526-025-03024-3
M3 - Article
AN - SCOPUS:105006729839
SN - 0944-2669
VL - 64
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 5
M1 - 172
ER -